Downlink multi-user MIMO (MU-MIMO) has been adopted in some recent wireless communication standards to enhance spectral efficiency, but it requires accurate channel state information at the transmitter (CSIT) to fully exploit its potential. In a frequency-division duplex (FDD) system, the obtaining of CSIT requires receiver feedback, and various CSI compression and feedback methods have been proposed in the literature. The present work considers an LTE-like scenario where the transmitter uses implicit CSI fed back by the receivers to reconstruct the MIMO channel coefficients, where the implicit CSI includes preferred precoding matrices and channel quality indications. To solve for the channel coefficients from these implicit CSI quantities, however, requires multiple feedbacks computed using different sounding pilots. We describe the overall design of the proposed method, formulate the corresponding mathematical problem of CSIT estimation, and derive a solution to the problem considering both time-invariant and time-varying channels. And we present some numerical results to illustrate the performance of the method.